This paper presents a variable damping controller to improve the trade-off between agility and stability in physical human-robot interaction (pHRI), while reducing user effort. Variable robotic damping, defined as a dual-sided logistic function, was determined in real time throughout a range of negative to positive values based on the user's intent of movement. To evaluate the effectiveness of the proposed controller, we performed a set of human experiments with subjects interacting with the end-effector of a 7 degree-of-freedom robot. Twelve subjects completed target reaching tasks under three robotic damping conditions: fixed positive, fixed negative, and variable damping. On average, the variable damping controller significantly shortened the rise time by 22.4% compared to the fixed positive damping. It is also important to note that the rise time in the variable damping condition was as fast as that in the fixed negative damping condition and there was no statistical difference between the two conditions. The variable damping controller significantly decreased the percentage overshoot by 49.6% and shortened the settling time by 29.0% compared to the fixed negative damping. Both the maximum and mean root-mean-squared (RMS) interaction forces were significantly lower in the variable damping condition than the other two fixed damping conditions, i.e., the variable damping controller reduced user effort. The maximum and mean RMS interaction forces were at least 17.3% and 20.3% lower than any of the fixed damping conditions, respectively. The results of this study demonstrate that humans can extract the benefits of the variable damping controller in the context of pHRI, as it significantly improves the trade-off between agility and stability and reduces user effort in comparison to fixed damping controllers.